Do Xbox Live Arcade games ever reduce in price, if they are older or during special sale events? I know Gold members get a deal-of-the-week but am unaware of anything beyond that.
Sometimes after a year or so there will be a permanent price drop, but there's no guarantee. And there are special deals every now and then, but you can't really predict what they will be. I keep track of this by subscribing to Joystiq's "Now Playing" RSS feed: http://www.joystiq.com/tag/now-playing/rss.xml
Every Tuesday they list the new releases for all consoles, including XBLA games and XBLA price changes. It's nice because I only have to look at it once a week. I'm sure there are other sites with similar content; Joystiq's just the one I'm familiar with.
You might also want to check out http://www.cheapassgamer.com, though I found it took a much bigger commitment to keep up with it.